%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET582^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:22:57 AM UTC 2026
% Result : Theorem 4.33s 2.59s
% Output : Refutation 4.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 11 unt; 0 typ; 3 def)
% Number of atoms : 208 ( 60 equ; 0 cnn)
% Maximal formula atoms : 12 ( 6 avg)
% Number of connectives : 360 ( 91 ~; 54 |; 36 &; 173 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 9 ^; 21 !; 0 ?; 33 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_decl,type,
sk1: a > $o ).
thf(sk2_decl,type,
sk2: a > $o ).
thf(sk3_decl,type,
sk3: a > $o ).
thf(sk4_decl,type,
sk4: a ).
thf(sk1_def,definition,
( sk1
= ( @+[A: a > $o] :
~ ! [B: a > $o,C: a > $o] :
( ! [D: a] :
( ( ( ~ ( A @ D ) )
= ( B @ D ) )
= ( C @ D ) )
=> ( A
= ( ^ [D: a] :
( ( ( B @ D )
& ~ ( C @ D ) )
| ( ( C @ D )
& ~ ( B @ D ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: a > $o] :
~ ! [B: a > $o] :
( ! [C: a] :
( ( ( ~ ( sk1 @ C ) )
= ( A @ C ) )
= ( B @ C ) )
=> ( sk1
= ( ^ [C: a] :
( ( ( A @ C )
& ~ ( B @ C ) )
| ( ( B @ C )
& ~ ( A @ C ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: a > $o] :
~ ( ! [B: a] :
( ( ( ~ ( sk1 @ B ) )
= ( sk2 @ B ) )
= ( A @ B ) )
=> ( sk1
= ( ^ [B: a] :
( ( ( sk2 @ B )
& ~ ( A @ B ) )
| ( ( A @ B )
& ~ ( sk2 @ B ) ) ) ) ) ) ) ) ).
thf(1,conjecture,
! [A: a > $o,B: a > $o,C: a > $o] :
( ! [D: a] :
( ( ( ~ ( A @ D ) )
= ( B @ D ) )
= ( C @ D ) )
=> ( A
= ( ^ [D: a] :
( ( ( B @ D )
& ~ ( C @ D ) )
| ( ( C @ D )
& ~ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_25_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > $o,B: a > $o,C: a > $o] :
( ! [D: a] :
( ( ( ~ ( A @ D ) )
= ( B @ D ) )
= ( C @ D ) )
=> ( A
= ( ^ [D: a] :
( ( ( B @ D )
& ~ ( C @ D ) )
| ( ( C @ D )
& ~ ( B @ D ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > $o,B: a > $o,C: a > $o] :
( ! [D: a] :
( ( ( ~ ( A @ D ) )
= ( B @ D ) )
= ( C @ D ) )
=> ( A
= ( ^ [D: a] :
( ( ( B @ D )
& ~ ( C @ D ) )
| ( ( C @ D )
& ~ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: a] :
( ( ( ( ~ ( sk1 @ A ) )
= ( sk2 @ A ) )
= ( sk3 @ A ) )
& ( sk1
!= ( ^ [B: a] :
( ( ( sk2 @ B )
& ~ ( sk3 @ B ) )
| ( ( sk3 @ B )
& ~ ( sk2 @ B ) ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
( sk1
!= ( ^ [A: a] :
( ( ( sk2 @ A )
& ~ ( sk3 @ A ) )
| ( ( sk3 @ A )
& ~ ( sk2 @ A ) ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
( ( ^ [A: a] :
( ( ( sk2 @ A )
& ~ ( sk3 @ A ) )
| ( ( sk3 @ A )
& ~ ( sk2 @ A ) ) ) )
!= sk1 ),
inference(lifteq,[status(thm)],[6]) ).
thf(9,plain,
( ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ( sk3 @ sk4 )
& ~ ( sk2 @ sk4 ) ) )
!= ( sk1 @ sk4 ) ),
inference(func_ext,[status(esa)],[8]) ).
thf(5,plain,
! [A: a] :
( ( ( ~ ( sk1 @ A ) )
= ( sk2 @ A ) )
= ( sk3 @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
! [A: a] :
( ( sk3 @ A )
= ( ( ~ ( sk1 @ A ) )
= ( sk2 @ A ) ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(15,plain,
( ( ( ( sk2 @ sk4 )
& ( ( ~ ( sk1 @ sk4 ) )
!= ( sk2 @ sk4 ) ) )
| ( ( ( ~ ( sk1 @ sk4 ) )
= ( sk2 @ sk4 ) )
& ~ ( sk2 @ sk4 ) ) )
!= ( sk1 @ sk4 ) ),
inference(rewrite,[status(thm)],[9,7]) ).
thf(17,plain,
( ( ( sk2 @ sk4 )
& ( ( ~ ( sk1 @ sk4 ) )
!= ( sk2 @ sk4 ) ) )
| ( ( ( ~ ( sk1 @ sk4 ) )
= ( sk2 @ sk4 ) )
& ~ ( sk2 @ sk4 ) )
| ( sk1 @ sk4 ) ),
inference(bool_ext,[status(thm)],[15]) ).
thf(23,plain,
( ( ( sk2 @ sk4 )
| ( ( ~ ( sk1 @ sk4 ) )
= ( sk2 @ sk4 ) )
| ( sk1 @ sk4 ) )
& ( ( sk2 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk1 @ sk4 ) )
& ( ( ( ~ ( sk1 @ sk4 ) )
!= ( sk2 @ sk4 ) )
| ( ( ~ ( sk1 @ sk4 ) )
= ( sk2 @ sk4 ) )
| ( sk1 @ sk4 ) )
& ( ( ( ~ ( sk1 @ sk4 ) )
!= ( sk2 @ sk4 ) )
| ~ ( sk2 @ sk4 )
| ( sk1 @ sk4 ) ) ),
inference(cnf,[status(esa)],[17]) ).
thf(24,plain,
( ( sk2 @ sk4 )
| ( ( ~ ( sk1 @ sk4 ) )
= ( sk2 @ sk4 ) )
| ( sk1 @ sk4 ) ),
inference(cnfConj,[status(thm)],[23]) ).
thf(28,plain,
( ( ( sk2 @ sk4 )
= ( ~ ( sk1 @ sk4 ) ) )
| ( sk2 @ sk4 )
| ( sk1 @ sk4 ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(52,plain,
( ( sk2 @ sk4 )
| ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ~ ~ ( sk1 @ sk4 ) ),
inference(bool_ext,[status(thm)],[28]) ).
thf(76,plain,
( ( sk2 @ sk4 )
| ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk1 @ sk4 ) ),
inference(cnf,[status(esa)],[52]) ).
thf(77,plain,
( ( sk2 @ sk4 )
| ( sk1 @ sk4 ) ),
inference(simp,[status(thm)],[76]) ).
thf(90,plain,
( ( sk1 @ sk4 )
| ( ( ( ( sk2 @ sk4 )
& ( ( ~ ( sk1 @ sk4 ) )
!= ( sk2 @ sk4 ) ) )
| ( ( ( ~ ( sk1 @ sk4 ) )
= ( sk2 @ sk4 ) )
& ~ $true ) )
!= ( sk1 @ sk4 ) )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[77,15]) ).
thf(91,plain,
( ( sk1 @ sk4 )
| ( ( ( sk2 @ sk4 )
& ( ( ~ ( sk1 @ sk4 ) )
!= ( sk2 @ sk4 ) ) )
!= ( sk1 @ sk4 ) )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk4 ) ) ),
inference(simp,[status(thm)],[90]) ).
thf(92,plain,
( ( sk1 @ sk4 )
| ( ( ( sk2 @ sk4 )
& ( ( ~ ( sk1 @ sk4 ) )
!= ( sk2 @ sk4 ) ) )
!= ( sk1 @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[91:[]]) ).
thf(113,plain,
( ( sk1 @ sk4 )
| ( ( sk2 @ sk4 )
& ( ( ~ ( sk1 @ sk4 ) )
!= ( sk2 @ sk4 ) ) )
| ( sk1 @ sk4 ) ),
inference(bool_ext,[status(thm)],[92]) ).
thf(120,plain,
( ( ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk1 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ( ( ~ ( sk1 @ sk4 ) )
!= ( sk2 @ sk4 ) )
| ( sk1 @ sk4 ) ) ),
inference(cnf,[status(esa)],[113]) ).
thf(122,plain,
( ( sk1 @ sk4 )
| ( ( ~ ( sk1 @ sk4 ) )
!= ( sk2 @ sk4 ) )
| ( sk1 @ sk4 ) ),
inference(cnfConj,[status(thm)],[120]) ).
thf(124,plain,
( ( ( sk2 @ sk4 )
!= ( ~ ( sk1 @ sk4 ) ) )
| ( sk1 @ sk4 )
| ( sk1 @ sk4 ) ),
inference(lifteq,[status(thm)],[122]) ).
thf(125,plain,
( ( ( sk2 @ sk4 )
!= ( ~ ( sk1 @ sk4 ) ) )
| ( sk1 @ sk4 ) ),
inference(simp,[status(thm)],[124]) ).
thf(128,plain,
( ( sk1 @ sk4 )
| ~ ~ ( sk1 @ sk4 )
| ( sk1 @ sk4 )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[77,125]) ).
thf(129,plain,
( ( sk1 @ sk4 )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk4 ) ) ),
inference(simp,[status(thm)],[128]) ).
thf(130,plain,
sk1 @ sk4,
inference(pattern_uni,[status(thm)],[129:[]]) ).
thf(134,plain,
~ ( ( ( sk2 @ sk4 )
& ( ( ~ $true )
!= ( sk2 @ sk4 ) ) )
| ( ( ( ~ $true )
= ( sk2 @ sk4 ) )
& ~ ( sk2 @ sk4 ) ) ),
inference(rewrite,[status(thm)],[15,130]) ).
thf(135,plain,
$false,
inference(simp,[status(thm)],[134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET582^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.20 % Computer : n009.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 13:38:00 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.05/0.81 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/1.00 % [INFO] Parsing done (181ms).
% 1.23/1.01 % [INFO] Running in sequential loop mode.
% 2.05/1.40 % [INFO] eprover registered as external prover.
% 2.05/1.41 % [INFO] Scanning for conjecture ...
% 2.21/1.50 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.21/1.54 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.21/1.54 % [INFO] Problem is higher-order (TPTP THF).
% 2.21/1.54 % [INFO] Type checking passed.
% 2.21/1.55 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 4.33/2.58 % [INFO] Killing All external provers ...
% 4.33/2.59 % Time passed: 2241ms (effective reasoning time: 1572ms)
% 4.33/2.59 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 4.33/2.59 % Axioms used in derivation (0):
% 4.33/2.59 % No. of inferences in proof: 30
% 4.33/2.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2241 ms resp. 1572 ms w/o parsing
% 4.58/2.67 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.58/2.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------